Sadly, Jonathan Coulton’s song contained in this Youtube video is now out of date. Benoit Mandelbrot, renowned mathematician, passed away this past Thursday at the age of 85.
I often mention fractals to explain to theists that infinite complexity can be derived from very simple math. This is an almost direct analog to how the laws of chemistry, as simple and wholly scrutable as they might be individually, could result in life spontaneously self-arranging. Nobody needs to have intelligently designed these laws, they emerge as complex behaviours from the simpler behaviours of electrons, protons and neutrons. And those, in turn, emerge as complex behaviours from the simpler ones of quarks, leptons, and other fundamental particles. And those, themselves, may well emerge from simpler forms, like in string theory. And whatever the fundamental thing of the universe is, could emerge unbidden from the universe’s zero-net-energy state. Or from some other simpler abstraction we have not yet discovered.
In this way I am convinced that this universe functions as like a fractal. That Benoit Mandelbrot discovered an equation that showed amazing complexity at infinite zoom levels doesn’t mean he intelligently designed the fractal to be infinitely complex, though it takes a keen mind to recognize that the whole abstraction of math as a concept, when visualized on graphing paper, could result in something so intricate, delicate and amazing as the Mandelbrot set fractal.